Turbulent mixing in stably stratified flows

by Hebert, David A

Abstract (Summary)

High resolution direct numerical simulations are used to investigate the dynamics of turbulence in flows subject to strong stable stratification, which are common in natural settings. Results are presented for two categories of simulations, uniform and non-uniform density stratification. For all simulated flows, the density stratification was held constant in time, and there was no ambient shear. Flows with uniform density stratification are first analyzed to help provide clear insight to physical processes, followed by flows with non-uniform density stratification which better represent the stratification occurring in nature. Areas of non-uniform density stratification include thermohaline staircases and atmospheric layer transitions. For uniform density gradient flows, it is observed that the Froude-Reynolds number scaling developed by Riley and de Bruyn Kops [2003] is similar to the buoyancy Reynolds number, Reb = Îµ/Î½N2 . This supports the use of two dimensionless parameters obtained from dimensional analysis to predict turbulence in a density stratified flow. Also, due to the intermittent nature of density stratified flows, an auto-correlation length scale may be more appropriate than the typical advective length scale L a = [Special characters omitted.] . Finally, the common assumption that kinetic energy dissipation rate Îµ can be approximated by the vertical shear is shown to be valid only when Re b â¤ [Special characters omitted.] (1). Non-uniformly stratified flows are often characterized simply by the average density change with height, which may not adequately describe the flow. For simulated wake flows with the same average density stratification, but altered vertical stratification profiles, the flow dynamics are seen to depend on the ratio Î¾ = Î´u /Î´ Ï , where Î´u and Î´Ï are characteristic wake and stratification vertical length scales. When Î¾ is monotonically increased from 0.01 (near linear stratification) to 2 (wake height is twice stratification height), typical stratified flow behavior is observed, such as reduced decay of kinetic energy and inhibited vertical motion. In contrast, when Î¾ > 2, a transition occurs and the flow demonstrates non-stratified qualities, including rapid decay of kinetic energy and minimal inhibition of vertical motion. In addition, a method for calculating available potential energy in non-uniform density stratified flows has been developed. It will be shown that mixing of available potential energy Ï is confined to the stratification layer, which supports the observation of large mixing in regions of salt fingering found by St. Laurent and Schmitt [1999] and Schmitt [2003].